The polynomial is .

First find the coefficients of the x-terms;

Find two numbers with a product of 1 and 81 is 81 and a sum is 18.

So, the two coefficients must be 9 and 9 since and 9 + 9 = 18. (Rewrite the expression using coefficients)

Apply associative property of addition: a + (b + c) = (a + b) + c

Find the Greatest Common factor (GCF) of each group.

Greatest Common factor (GCF) of is x.

Greatest Common factor (GCF) of is 9.

                           (Factor out the GCF)

Rewrite the expression using Distributive Property

The polynomial is a perfect square trinomial.

Yes, the polynomial is a perfect square trinomial.